Normalize the number 277. using the the real IEEE float values 
    1 bit sign, 10 bit exponent, 7 bit significand
 
First convert to binary. 
  277
  138 1  lsb
   69 0
   34 1
   17 0
    8 1
    4 0
    2 0
    1 0
    0 1  msb

   100010101b

Represent in the equivalent of scientific notation,.

   (1).00010101 b * 2^8
       -------      <-   7 significant bits.
   
Generating a bias.

  Use formula 2^(n-1) - 1 where n is the size of the exponent.
    2^(10-1)-1 = 511 bias

Biasing this exponent gives :

  8 + 511 = 519 

      519
- 1 * 512
      ---
      007
- 0 * 256
      ---
      007
- 0 * 128
      ---
      007
- 0 * 064
      ---
      007
- 0 * 032
      ---
      007
- 0 * 016
      ---
      007
- 0 * 008
      ---
      007
- 1 * 004
      ---
      003
- 1 * 002
      ---
      001
- 1 * 001
      ---
      000

      10 0000 0111

      (512*1+4*1+2*1+1*1)
       512  +4  +2  +1   = 519

Sign bit 0 (positive)
Biased Exponent 10 0000 0111
Significand 0001 0101 0000 0000 
  Remember, when normalizing, we don't record the most significant bit. 

Floating point 0 1000000111 0001010

* Unlike integer storage, an integer with a large number of significant
  digits may not be stored exactly in float storage.

  So, using float to store a very large integer may not be best solution.
Conversion back